$\begin{cases} f(1)=4 \\\\ f(n)=f(n-1)\cdot(-0.5) \end{cases}$ Find an explicit formula for $f(n)$. $f(n)=$
From the recursive formula, we can tell that the first term of the sequence is ${4}$ and the common ratio is ${-0.5}$. This is the explicit formula of the sequence: $f(n)= {4}\cdot( {-0.5})^{{\,n-1}}$ Note that this solution strategy results in this formula; however, an equally correct solution can be written in other equivalent forms as well.